Modeling of Multi-Physics Phenomena in Fast Reactors ...lib.aeoi.org.ir/Content/downloads/Confrences_FR13/C_10/10-2-.pdfC/R Driving Rod 1st Baffle Plate Core Instruments Plate (CIP)

H. Ninokata - Nuclear Reactors Group

2013.02.05 FR13, Paris

2013.03.05 FR13, Paris

Hisashi NINOKATA

Politecnico di Milano

Department of Energy

CeSNEF-Nuclear Engineering Division

Nuclear Reactors Group

Modeling of Multi-Physics Phenomena in Fast Reactors

Design/Safety and Experimental Validation

International Conference on Fast Reactors

and Related Fuel Cycles (FR13)

4-7 March 2013, Paris, France

Hisashi Ninokata,

Hideki Kamide,

Marco Pellegrini

Marco Ricotti

2013.02.05 FR13, Paris

Multi-physics phenomena of concern

Characterized by time-space scales − Microscopic

− Mesoscopic

− Macroscopic

− Global scales

Described by mass fields (components), flow fields, temperature fields − Homogeneous mixture model

− Multi-fluid model or multi-fluid multi-field model

Coupled with chemical reactions, structural mechanics, material sciences − Chemical reactions … Na burning, Na-H2O,

− Fluid-structure interactions … chemical, mechanical, thermal

Taking place when fast reactors are under − S.S. full power operations: cavitation, erosion, corrosion, FP deposition, crud

sedimentation, thermal striping/stratification,

− DHR conditions

− Transient conditions

− Accident conditions: fuel S/A degradation, core meltdown and relocation

2013.01.25 9:30-1030

Bovisa

MULTI-PHYSICS PHENOMENA MODELING

(NOTES ARE FROM OR BASED ON THE INFORMATION FROM JAEA)

Examples:

1. High cycle thermal fatigue in JSFR: Coupling of CFD and FEM

2. Sodium water reaction

3. Fuel S/A degradation and CDAs

Topics 1

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Bovisa

High Cycle Thermal Fatigue at TOP Core Instrumentation Plate

Thermal Fatigue caused by Thermal Mixing between

- Hot Sodium from Fuel Subassemblies and

- Cold sodium from Control Rod Channels and Blanket Fuel Subassemblies

Backup Control Rod

(BCR)Primary Control Rod

Fuel Subassembly (FS)

Electromagnet

for SASSC/R

Driving

1st Baffle Plate

Core Instruments

Plate (CIP)

Flow-hole

Sodium

Cold Sodium

from C/R(UIS)

Target Areas

Concerning about

Thermal Fatigue

(Top view image

around a control

rod channel)

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Bovisa

Japan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy AgencyJapan Atomic Energy Agency

②Local analysis Local analysis around

PCR of JSFR

①Whole upper plenum analysis

③Thermal stress analysis

（for CRs）（for BFs）

Temperature information in structure

Boundary conditions for local analysis

③Estimation of structural integrity

by thermal stress analysis (FINAS)

①Thermal-hydraulics in upper plenum

by RANS - UIS external flow for blanket fuels

- UIS internal flow for control rods

② Fluid-structure thermal interaction

LES and heat conduction in structure

simulation by MUGTHES in local areas

around - Control rod (CR) channels

- Blanket fuel (BF) subassemblies

Numerical Estimation Method for Thermal Fatigue on CIP

~ Fluid-Structure Thermal Interaction Simulation ~

2013.01.25 9:30-1030

Bovisa

Numerical Simulations of Thermal Mixing

in WATLON T-Pipe as Validation

262,632 cells Main pipe Branch pipe

Inner Diameter: 0.15 m(=Dm) 0.05 m(=Db)

Inlet Temperature: 48℃ (=Tm) 33℃ (=Tb)

Mean Velocity:

(Impinging jet case) 0.26 m/s(=Wm) 1.0m/s(=Vb)

(Wall jet case) 1.46 m/s(=Wm) 1.0m/s(=Vb)

Main pipe flow

Branch pipe flow

噴流の向き

0.01 0.1 1 10 100

Mb (kg.m/s2)

Mr < 0.35 (◆：Impinging jet)

0.35<Mr<1.35

(●：Deflecting jet)

Mr > 1.35 (■：Wall jet)Mr = Mm/Mb

(Low Main Flow: Impinging Jet)

(High Main Flow: Wall Jet)

○4,000 data at 1kHz sampling during last 4 seconds

in 10 seconds transient calculation

Flow-pattern map

Jet direction

Main pipe flow:

Branch pipe flow:

mbmmm WDDM

224 bbbb VDM

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Bovisa

Typical Numerical Results of Fluid Temperature Distributions

at Impinging Jet and Wall Jet Cases in WATLON

Impinging jet case

Wall jet case

0.0 0.2 0.4 0.6 0.8 1.0

(T -T b )/dT , T' /dT

Experiment, (T-Tb)/dT

LES(Cs=0.14),

Experiment, T'/dT

LES(Cs=0.14),

(T -T b )/dT

T' /dT

0.0 0.2 0.4 0.6 0.8 1.0

(T -T b )/dT , T' /dT

Experiment, (T-Tb)/dT

LES(Cs=0.14), (T-Tb)/dT

Experiment, T'/dT

LES(Cs=0.14), T'/dT

(T -T b )/dT

T' /dT

temperature large-scale eddy structure

2013.01.25 9:30-1030

Bovisa

(NOTES ARE FROM OR BASED ON THE INFORMATION FROM JAEA)

Examples:

1. High cycle thermal fatigue in JSFR

2. Sodium water reaction: wastage, failure propagation

3. Fuel S/A degradation and CDAs

Topics 2

2013.01.25 9:30-1030

Bovisa

Sodium-Water Reaction (SWR) Accident

Water side: about 15 MPa

Shell side: 0.2 MPa

Safety assessment of steam generator (SG) in sodium-cooled fast reactor

SG (evaporator)

in Monju

Reacting jet Na

Failed tube Adjacent tube

Sodium-water reaction

Water,

Erosion

Combination

Strength

degradation

Wastage

Over-heating rupture

Secondary failure (failure propagation)

Multi-physics nature: thermal hydraulics, multiphase flow, chemical reaction,

structure, material complex

Progression of damage

Evaluation of possibility of propagation

most important issue

2013.01.25 9:30-1030

Bovisa

Evaluation of Failure Propagation

Final goal is to evaluate

wastage environment

wastage rate

possibility of failure propagation

Evaluation for SG in prototype FR A large number of mock-up tests

Evaluation for SG in commercial FR Numerical analysis and minimal

mock-up test

Analytical evaluation system

(1) SERAPHIM

Analysis of compressive

multicomponent multiphase

flow with SWR

(2) TACT

Analysis of target tube heat

transfer and stress, evaluation of

wastage rate and failure

propagation

(3) RELAP5

Analysis of boiling two-phase flow

Wastage

environment

2013.01.25 9:30-1030

Bovisa

Numerical Methods in SERAPHIM

Finite difference method

3D Cartesian coordinate (x, y, z), 2D cylindrical coordinate (r, z)

Multi-fluid model (water, liquid sodium and multi-component gas)

HSMAC method (modified for compressible multiphase flow)

Phase change model

EOS: Modified Benedict-Webb-Rubin equation

Surface reaction model (gas-liquid reaction)

Gas-phase reaction model (gas-gas reaction)

Compressible multiphase flow model

Sodium-water chemical reaction model

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Bovisa

Surface Reaction Model

Surface reaction = Chemical reaction at interface between water vapor and liquid sodium

Model assumptions

Na(l) + H2O(g) NaOH(l) + 1/2H2(g)

Infinite reaction rate (progress of chemical reaction is limited

by mass flow rate of reactant gas toward interface)

Reaction products move to gas phase

Reaction heat is added to gas phase

Na(liquid)

Interface

Multicomponent gas:

H2O, Na(gas), NaOH(aerosol),

NaOH(gas), H2

Mass flow rate

DSh jg

2013.01.25 9:30-1030

Bovisa

Numerical results for the SWAT-1R test

Experiment Calculation

(weight averaged) (measured) Cylindrical vessel

filled with liquid

sodium

Diameter: 0.4 m

Height: 1.8 m

43 tubes

Water vapor

leaks from the

lowest tube and

goes upward

Conditions of

water vapor:

17.0 MPa,

352 oC

Conditions of

sodium:

0.2 MPa,

470 oC

Void fraction Computational Domain

Gas phase goes upward

Temperature Field

High temperature region

expands to upper left both in

the experimental result and the

numerical result.

2013.01.25 9:30-1030

Bovisa

(NOTES ARE FROM OR BASED ON THE INFORMATION FROM JAEA;

AND TOKYO INSTITUTE OF TECHNOLOGY R&D RESULTS)

Examples:

1. High cycle thermal fatigue in JSFR

2. Sodium water reaction

3. Fuel S/A degradation and CDAs: calculation quality depends on the physical models

Topics 3

2013.01.25 9:30-1030

Bovisa

Computational model

SAS/SIMMER code system for CDAs since 1970’s

KAMUI – for fuel S/A degradation by subchannel analysis

Multi-component multi-phase flow Multi-component multi-field formulation

In case of fuel S/A degradation: 3 components, 3-phases and 2- or 3-velocity fields (mixture velocity fields):

[ex] Liquid-phase and solid-phase assigned to one field and gas-phase to the other;

Mixture fields required mixture material properties (viscosity, heat capacity, conductivity, .. etc.)

Phase interfaces --- topology

Lumped modeling of heat, momentum and mass transfers at the phase interfaces among all components; all from experiment

Component Solid-phase Liquid-phase Vapor-phase

Fuel X X X

Steel X X X

Sodium X X

(2velocity fields) Mixture velocity field Gas-phase v

2013.01.25 9:30-1030

Bovisa

In-Pile Experiment

SCARABEE

EBR-II

IGR-EAGLE (Experimental Acquisition of Generalized Logic to

Eliminate criticalities)

2013.01.25 9:30-1030

Bovisa CDA Evaluation Methods & Mitigation Measures

- IGR (Impulse Graphite Reactor) in EAGLE Project -

Reactor core

Cooling water cavity

Control rod

channel

Cross-section of IGR core

(NNC in Kazakhstan)

PERFORMANCE

Max. thermal neutron flux density:

Max. thermal neutron fluence:

Min. half-width of pulse:

Max. energy release:

Central Experimental Channel (CEC):

7×1016 n/cm2s

3.7×1016 n/cm2

0.12 s

5.2 GJ

φ228mm×L3825mm

2013.01.25 9:30-1030

Bovisa CDA Evaluation Methods & Mitigation Measures

- Upward Discharge Experiment in EAGLE Project -

Insertion of test section into IGR core

Test section for

upward discharge

Inner duct

SA can wall

section

Discharge path

Closed end

FAIDUS option

(reference for JSFR)

IGR core

Fuel pins to be molten

Simulated core part

Discharge path

Simulated upper plenum Sodium

2013.01.25 9:30-1030

Bovisa

Validation of subassembly degradation and core

meltdown_relocation models

CABRI hodo-scope data

SCARABEE TIB

temperature flow data

TREAT/SLSF

Flow blockage at the start of transient

Coolant

Fuel pin

6 5 4 3

14 13 12 11 10 9 8 7

19 18 17 16 15

Fissile length 60cm

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Bovisa

0 2 4 6 8 10 12 14 16 18 20 22 24

tim e (sec)

flow rate (m3/h)

BE+2 outflow

0 2 4 6 8 10 12 14 16 18 20 22 24

tim e (sec)

temperature (C)

tcool(4,9)tcool(4,10)tcool(4,11)

0 2 4 6 8 10 12 14 16 18 20 22 24

tim e(sec)

tclad(1,9)tclad(1,10)tclad(1,11)

Time (sec)

Computation

Coolant T (S/A

peripheral)

Exit flow

Multi-component multi-field model validation for

SCARABEE-BE+2 Experiments -2 (TIB)

Cladding T (S/A

center)

2013.01.25 9:30-1030

Bovisa

Liquid

Sodium

Clad Clad Fuel

Liquid

Sodium

Liquid

Blockage

５ｓ７ｓ

Good agreement for the onset timings of sodium boiling

and cladding melting-relocation

S/A Centerline

S/A wall

2013.01.25 9:30-1030

Bovisa

１５ｓ

Fuel Clad

Liquid

Sodium

Liquid

Blockage

Fuel Particle

S/A center fuel melting_relocation.

S/A peripheral fuels no melting →

agreement with the experiment

2013.01.25 9:30-1030

Bovisa

SCARABEE-BE+2 Experiments -5

Subchannel analysis results

KAMUI BE+2

KAMUI APL

Agreement? Excellent, good, fair, poor?

Trend agreement is important but meaningless if the users

don’t try to catch physics

To minimize subjective judgment on modeling multi-

physics, we need:

Identification and estimation of uncertainties

Only visual comparisons are not sufficient

2013.01.25 9:30-1030

Bovisa

H. Ninokata and E.

Merzari 25

How do you catch physics?

I. In case of DNS or LES

So much information from DNS or LES

Many new phenomena, detailed turbulent structure through visualization …

Done by visualization thanks to rapid progresses in CG technology …. Fancy -- but it’s a subjective approach

Objective education techniques, to avoid possible controversy and to identify nature and significance of the structure

Ex. Proper Orthogonal Decomposition Technique

2013.01.25 9:30-1030

Bovisa

H. Ninokata and E.

Merzari 26

To identify the motions which contain the most energy.

Lumley (1967) Berkooz, Holmes & Lumley (1993), Holmes et al, (1996)

Based on the Karhunen-Loeve expansion, a basic tool in pattern recognition;

DNS (or LES) data: <U(x)>+u(x,t); Energy: u2

Principle:

− Expand u(x,t) by the orthogonal functions; u(x,t) ~ San(t)jn(x)

− Maximize u2 : Orthogonal functions as a weighting function;

− The process reduced to an Eigen-value problem (l1>l2>l3, …>lN>...);

− Higher order terms can be curtailed: a partial sum is sufficient

Therefore the maximization problem automatically selects the decomposition that contains the highest amount of energy in the first few modes. It allows us to truncate the expansion at low values of N

POD: Proper Orthogonal Decomposition

2013.01.25 9:30-1030

Bovisa

H. Ninokata and E.

Merzari 27

How do you catch physics?

II. In case of multi-physics simulation

As more multi-physics involved, more complex calculation system with so many physical models representing the interactions

Physical models are based on known knowledge and a result of assumptions, approximations, compromises

With the CV sizes larger, more uncertainties

Comparisons must be done with experiment (and theory if any), Done by visualization – Not sufficient

Needs to identify modeling uncertainties, to avoid possible controversy and to identify nature and significance of the structure

An attempt to quantify uncertainty

2013.01.25 9:30-1030

Bovisa

Uncertainty identification in physical modeling -1

Erroneous example: stratification in sodium flow

turbulence heat flux model should take into account the gravity

We would like to know how erroneous the predictions are when the turbulent heat

flux is modeled w/ or w/o gravity effects

We follow the Bayesian rule P(B|A)={P(A|B)*P(B)}/P(A)

Prior probability P(B) [calculation] can be updated to P(B|A) with P(A), probability of

A by experimentation, where P(A|B) a likelihood function;

Noted that the likelihood P(A|B) is given a’priori but subjective; should be improved

by optimal estimation-control theories

2013.01.25 9:30-1030

Bovisa

Assume a degree of being subjective for a certain model, P(B),

P(B) could be updated based on a direct comparison of the model prediction with

experiment, to P(B|A)

By carrying out as many as calculations as possible with different model parameter

values, we obtain P(B|A)

P(B|A) accounts also for the uncertainty in the experimental results P(A) and

provides statistical information on the mean value, standard deviation, tolerance

limits, ..

2013.01.25 9:30-1030

Bovisa

A Simple Example:

Suppose the model for the turbulent heat flux in a CFD code is expressed in terms of velocity gradient (C1) and the gravity effect (C3)

Run as many cases for C1 and C3 as possible (Monte Carlo or economical Latin Hypercube Sampling) to construct a response surface

Mean value of C1 and C3 represent optimal values while the standard deviation could be interpreted as a subjective degree of belief in C1 and C3 model parameters.

C1 trustable; C3 questionable …….. Note: this is just an example

2013.01.25 9:30-1030

Bovisa Final Comments

• Focused on the current practices of numerical modeling and simulations

of thermal hydraulic phenomena in sodium-cooled fast reactor systems

• All these multi-physics simulation models have been subject to on-going

validation programs

• In practice, validation of engineering multi-physics phenomena is likely to

be made on rather qualitative basis, often relying on many subjective

judgments in comparison with the results from large-scale integral tests or

mock-up experiments

• In validation processes, although an eventual subjective judgment cannot

be ruled out but should be made minimal. To make it more quantitative

and rational, a proposal has been made of the identification of errors

and/or uncertainties inherent in computations based on the Bayesian rule

2013.01.25 9:30-1030

Bovisa 2013.01.25 9:30-1030

Bovisa

Hisashi NINOKATA

Politecnico di Milano

Department of Energy

CeSNEF-Nuclear Engineering Division

Nuclear Reactors Group

Thank you!

2013.01.25 9:30-1030

Bovisa

Modeling wall friction; Interfacial friction

1/2 2, , 1/2

WL Z f fi l Wh L

( ) ,Re

fhff DG /Re

Fluid mixture wall friction factor

: two phase flow pressure drop multiplier

f: mixture viscosity

wwwwCnL

zI11112/1

1 1/2 1/2

, , ,, 1/2

n nIL z I z I zi l

1/2 1/2

, , ,, 1/2

n nIG z I z I zi l

A I,z：Interfacial area concentration; ρG：vapor density; Cf：Interfacial friction factor

(Wallis) ; w： axial velocity

A I,z ： α > 0.6 annular flow model

0.6 > α > 0.4 Ishii & Chawla for slug flows

0.4 > α Ishii & Chawla for bubbly flow model

2013.01.25 9:30-1030

Bovisa

Heat transfers

Between solid wall and liquid (sodium, liquid phase of steel,

MOX fuels)

− HT correlations for liquid metals

Between solid wall and vapor-gas

− Dittus-Boelter etc.

Between fluid and different fluid (sodium/molten steel,

sodium/molten fuel, molten fuel/molten steel, etc)

Between liquid and vapor-gas (Interfacial heat transfer and

heat transfer with interfacial mass transfer)

Radiation heat transfer

Modeling of Multi-Physics Phenomena in Fast Reactors ...lib.aeoi.org.ir/Content/downloads/Confrences_FR13/C_10/10-2-.pdfC/R Driving Rod 1st Baffle Plate Core Instruments Plate (CIP)

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